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The Best Writing on Mathematics 2020 (The Best Writing on Mathematics, 13) PDF

261 Pages·2020·18.289 MB·English
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The BEST WRITING on MATHEMATICS 2020 The BEST WRITING on MATHEMATICS 2020 Mircea Pitici, Editor princeton university press princeton and oxford Copyright © 2020 by Princeton University Press Princeton University Press is committed to the protection of copyright and the intellectual property our authors entrust to us. Copyright promotes the progress and integrity of knowledge. Thank you for supporting free speech and the global exchange of ideas by purchasing an authorized edition of this book. If you wish to reproduce or distribute any part of it in any form, please obtain permission. Requests for permission to reproduce material from this work should be sent to permissions @press .princeton .edu Published by Princeton University Press 41 William Street, Princeton, New Jersey 08540 6 Oxford Street, Woodstock, Oxfordshire OX20 1TR press .princeton .edu All Rights Reserved ISBN 9780691207575 ISBN (pbk.) 9780691207568 ISBN (e- book) 9780691213651 British Library Cataloging- in- Publication Data is available Editorial: Susannah Shoemaker and Kristen Hop Production Editorial: Nathan Carr Text Design: Carmina Alvarez Jacket/Cover Design: Chris Ferrante Production: Jacquie Poirier Publicity: Matthew Taylor and Katie Lewis Copyeditor: Paula Bérard This book has been composed in Perpetua Printed on acid- free paper. ∞ Printed in the United States of America 1 3 5 7 9 10 8 6 4 2 to the front- end management of the Ithaca Wegmans supermarket, for making a difference to me and to my family—twice Contents Color illustration insert follows page 128 Introduction Mircea Pitici ix Outsmarting a Virus with Math Steven Strogatz 1 Uncertainty Peter J. Denning and Ted G. Lewis 8 The Inescapable Casino Bruce M. Boghosian 15 Resolving the Fuel Economy Singularity Stan Wagon 29 The Median Voter Theorem: Why Politicians Move to the Center Jørgen Veisdal 39 The Math That Takes Newton into the Quantum World John Baez 45 Decades- Old Computer Science Conjecture Solved in Two Pages Erica Klarreich 54 The Three- Body Problem Richard Montgomery 61 The Intrigues and Delights of Kleinian and Quasi- Fuchsian Limit Sets Chris King 78 Mathematical Treasures from Sid Sackson Jim Henle 92 The Amazing Math Inside the Rubik’s Cube Dave Linkletter 108 viii Contents What Is a Hyperbolic 3- Manifold? Colin Adams 115 Higher Dimensional Geometries: What Are They Good For? Boris Odehnal 122 Who Mourns the Tenth Heegner Number? James Propp 137 On Your Mark, Get Set, Multiply Patrick Honner 145 1994, The Year Calculus Was Born Ben Orlin 153 Gauss’s Computation of the Easter Date Donald Teets 160 Mathematical Knowledge and Reality Paul Thagard 172 The Ins and Outs of Mathematical Explanation Mark Colyvan 189 Statistical Intervals, Not Statistical Significance Gerald J. Hahn, Necip Doganaksoy, and William Q. Meeker 198 Contributors 205 Notable Writings 213 Acknowledgments 225 Credits 227 Introduction Mircea Pitici This anthology is the 11th in the annual series of The Best Writing on Mathe- matics. It contains pieces originally published in late 2018 and throughout 2019 in various venues, including specialized print and online maga- zines, research journals, newspapers, books, and collections of confer- ence proceedings. The volume should be considered by the readers in conjunction with the other ten previously published in the series. Overview of the Volume In a piece eerily reminding us of the current coronavirus health crisis, Steven Strogatz recounts the little- known contribution of differential equations to virology during the HIV crisis and makes the case for con- sidering calculus among the heroes of modern life. Peter Denning and Ted Lewis examine the genealogy, the progress, and the limitations of complexity theory—a set of principles developed by mathematicians and physicists who attempt to tame the uncertainty of social and natural processes. In yet another example of fusion between ideas from mathematics and physics, Bruce Boghosian describes how a series of simulations carried out to model the long- term outcome of economic interactions based on free- market exchanges inexorably leads to extreme inequality and to the oligarchical concentration of wealth. Stan Wagon points out the harmonic- average intricacies, the practi- cal paradoxes, and the policy implications that result from using the miles- per- gallon measure for the fuel economy of hybrid cars. Jørgen Veisdal details some of the comparative reasoning supposed to take place in majoritarian democracies—resulting in electoral strat- egies that lead candidates toward the center of the political spectrum.

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